Monday’s Holiday

Posted on 6 October 2023 by RobertLovesPi

Banks, the U.S. bond market, and the U.S. Post Office will all be closed on John Lennon’s birthday this year (Monday, October 9th).

A Pair of Polyhedra Derived From the Snub Archimedeans

Posted on 4 October 2023 by RobertLovesPi

To make the polyhedron shown above, I started with a snub cube, then augmented all the triangular faces with prisms. Next, I formed this augmented solid’s convex hull, and, finally, I used the “try to make faces regular” function of the software I use to manipulate polyhedra (Stella 4d, which you can try here). The regular faces are the octagons and the small triangles.

I used the same process to make the polyhedron below, except that I started with the snub dodecahedron.

Clusters of Rhombic Triacontahedra

Posted on 2 October 2023 by RobertLovesPi

Here’s a rhombic triacontahedron, possibly the most well-known of the Catalan solids. It’s thirty faces are all golden rhombi (rhombi with their diagonals in the golden ratio).

Here’s what you get if you augment each face with another rhombic triacontahedron:

Coloring this cluster-polyhedron by face type has this result:

So what happens if each face of this cluster-polyhedron is augmented by another rhombic triacontahedron? This does:

Here’s another view of that, in “rainbow color mode”:

I made these virtual models with Stella 4d: Polyhedron Navigator. If you’d like to try this software for free, the website to visit is http://www.software3d.com/Stella.php.